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Alternative goodness-of-fit tests for linear models


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/10327

Alternative goodness-of-fit tests for linear models

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Title: Alternative goodness-of-fit tests for linear models
Author: Sun, Siu Kei
Advisor(s): Christensen, Ronald
Committee Member(s): Huerta, Gabriel
Fugate, Michael
Bedrick, Edward
Department: University of New Mexico. Dept. of Mathematics and Statistics
Subject: Fourier transforms, Lack-of-fit tests, Linear models
LC Subject(s): Linear models (Statistics)
Goodness-of-fit tests.
Fourier transformations.
Regression analysis--Asymptotic theory.
Forests and forestry--Measurement--Statistical methods.
Degree Level: Doctoral
Abstract: Fan and Huang (2001) presented a goodness-of-fit test for linear models based on Fourier transformations of the residuals of the fitted model. We present two more theoretically appealing tests in which the Fourier transforms are incorporated into a fitted model. We show that when suitably normalized, the new test statistics have the same asymptotic distribution as Fan and Huang's test. We propose modifications to the asymptotic normalization constants to improve the small sample sizes of our tests while retaining their asymptotic distributions. Small sample sizes and powers are examined via simulations. Real data of short-leaf pines from Bruce and Schumacher (1935) are used to illustrate the performance of the proposed tests.
Graduation Date: December 2009
URI: http://hdl.handle.net/1928/10327

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